XOR combination between the bits of a string

Question

Given an integer n, we can construct $2^n$ strings of length n. We can take the first element for each of these strings and create a list. In total 'n' such lists are possible. But now I need to create lists that are the XOR combinations of the n lists created. If n is 3 and abc is the string then I need to calculate a$oplus$b, a$oplus$c, c$oplus$b, a$oplus$b$oplus$c. How do I do this for a general n?
Here's the code so far...
n = 4; s = Tuples[{0, 1}, n]; a = Table[s[[i, j]], {j, 1, n}, {i, 1, 2^n}]
a gives the first four indices of all the strings. Now I need to calculate all the XOR combinations possible between these four lists.

kglr · Accepted Answer

Maybe
xOrCombinations[n_] := BitXor @@@ Subsets[Transpose @ Tuples[{0, 1}, n], {2, n}]

xOrCombinations[4] // MatrixForm // TeXForm

$$left(
begin{array}{cccccccccccccccc}
 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 
 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 
 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 
 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 
 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 
 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 
 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 
 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 
 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 
 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 
 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 
end{array}
right)$$
Also
xOrCombinations2[n_] := Mod[Plus @@@ Subsets[Transpose@Tuples[{0, 1}, n], {2, n}], 2]

xOrCombinations2[4] == xOrCombinations[4]

True

XOR combination between the bits of a string

One Answer

Add your own answers!

Ask a Question